US7251592B1 - Boundary layer transition model - Google Patents
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- US7251592B1 US7251592B1 US10/921,486 US92148604A US7251592B1 US 7251592 B1 US7251592 B1 US 7251592B1 US 92148604 A US92148604 A US 92148604A US 7251592 B1 US7251592 B1 US 7251592B1
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- the invention relates to computational fluid dynamics (CFD). More particularly, the invention relates to the design of airfoils for turbomachinery.
- CFD computational fluid dynamics
- turbomachines feature sections characterized by alternating circular arrays (often referred to as “rows”) of airfoils. Alternating, oppositely-oriented, rows of rotating blade and fixed vane airfoils may be present in any given section. Performance of the turbomachine is influenced by the size, positioning, and shape of these airfoils. CFD means are commonly used to optimize parameters for desired performance (e.g., efficiency) in desired operating conditions.
- the behavior of boundary layers, especially on the suction sides of the airfoils strongly influences airfoil performance.
- the boundary layer will start as a laminar flow and then typically transition to a turbulent flow.
- the boundary layer may also separate from the airfoil. The separated boundary layer may then reattach.
- Standard practice in the industry is to perform CFD simulations solving the Reynolds Average Navier-Stokes equations with a two-equation turbulence model.
- the turbulence model is disabled in the laminar portion of the boundary layer.
- the former is straightforward and may be done by analyzing the flowfield resulting from a converged CFD solution, which used either fully laminar or fully turbulent models. The latter is more difficult.
- one aspect of the invention involves a method for analyzing performance of a body (e.g., an airfoil).
- An estimated laminar separation location of a flow separating from the airfoil is determined.
- Freestream turbulence intensity is determined.
- a momentum thickness is determined.
- a turbulence length scale is determined.
- a first momentum thickness Reynolds number associated with a first estimate of the laminar/turbulent boundary layer transition location along the airfoil is determined. If the laminar separation location is downstream of the first estimate transition location, the first estimated transition location is used to determine a spatial domain for running a turbulent flow model.
- a second estimated transition location is used to determine a spatial domain for running the turbulent flow model.
- the second estimated transition location is determined as a function of a momentum thickness Reynolds number associated with the estimated laminar separation location.
- the determination of the laminar separation location may include determining an arc distance from a stagnation point to the laminar separation location.
- the determination of the second estimated laminar/turbulent boundary transition location may include determining a distance of the second estimated laminar/turbulent boundary transition location from the estimated laminar separation location as a constant multiplied by a streamwise position of the estimated laminar separation location and multiplied by an exponent of a momentum thickness based Reynolds number associated with the estimated laminar separation location.
- the exponent may be ⁇ (1.22-1.32).
- the constant may be 211-221.
- FIG. 1 is a schematic sectional view of an airfoil in a flowfield.
- FIG. 2 is a graph showing the calculation of the onset value of momentum thickness-based Reynolds number.
- FIG. 3 is a graph of such calculated Reynolds number against a composite turbulence and momentum parameter along with experimental data points.
- FIG. 4 is a graph of a prior art calculated Reynolds number against turbulence along with the experimental data points.
- FIG. 5 is a schematic sectional view of an airfoil with a separated/reattached boundary layer.
- FIG. 6 is a schematic sectional view of an airfoil with a separated boundary layer.
- FIG. 7 is a graph of calculated values of a quotient of a separation-to-transition distance divided by a separation streamwise location against a momentum thickness-based Reynolds number at the separation location.
- FIG. 8 is a graph of a prior art calculated Reynolds number against the product of a turbulence intensity with an exponent of a turbulence length scale divided by a separation-to-transition length.
- FIG. 9 is a flowchart of a CFD modeling procedure.
- FIG. 10 is a graph showing iteration history of a separation-to-transition distance.
- FIG. 11 is a plot of loss against Reynolds number for an exemplary airfoil.
- FIG. 12 is a schematic sectional view of baseline and reengineered airfoils.
- FIG. 13 is a plot of suction side curvature distribution against normalized streamwise distance for the airfoils of FIG. 12 .
- a missing element from prior transition modeling is the turbulence length scale ⁇ X which may be measured at the boundary layer edge. We have determined that this parameter, along with the turbulence intensity and momentum thickness, may be used to predict the transition from laminar to turbulent conditions.
- the momentum thickness-based Reynolds number may be identified as:
- ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ U ⁇ ⁇
- ⁇ the momentum thickness at such location
- ⁇ the density at the boundary layer edge at such location
- U ⁇ the flow velocity at the boundary layer edge at such location
- ⁇ the viscosity at the boundary layer edge at such location.
- the turbulence intensity may be identified as:
- the forgoing transition model may be applied to modeling the performance of an airfoil 20 ( FIG. 1 ) and optimizing the shape of such airfoil for a desired operating condition or range of conditions.
- the airfoil 20 has a leading edge 22 and a trailing edge 24 and pressure and suction side surfaces 26 and 28 .
- the airfoil is located in a flowfield 500 having a generally downstream direction 502 .
- the boundary layer may extend aft along each of the surfaces 26 and 28 .
- boundary layer modeling is critical on the suction side 28 and is often ignored on the pressure side 26 .
- the principles of the invention may also be applied to pressure side modeling.
- a laminar upstream portion 30 of the suction side boundary layer extends downstream from a stagnation point at the leading edge 22 .
- a transition location 32 divides the laminar portion from a downstream turbulent portion 34 .
- the boundary layer edge or boundary has associated upstream and downstream portions 36 and 38 in the laminar and turbulent regions.
- a streamwise distance S is shown along the suction side measured downstream from the leading edge stagnation point.
- the input conditions at locations 504 upstream of the airfoil are known or assumed.
- these conditions may be known from measurement or modeling of the engine combustor at a target operating condition.
- the upstream conditions may be taken from the conditions at downstream location 506 of the row thereahead. Modeling of the various rows may, thus, occur simultaneously in a similar fashion.
- An exemplary implementation may involve a first process for obtaining an initial estimated transition location.
- a first step is the generation of an appropriate CFD mesh whose boundaries are defined by the airfoil under consideration and the flowpath in which the airfoil resides.
- the CFD mesh will not contain flow property information until a first initialization process is performed using the known or assumed upstream and downstream flow conditions.
- the turbulence model is turned on throughout the flowfield including the areas which might end up being within the boundary layer portions 30 and 34 .
- the model may be run until convergence.
- the data is analyzed. The analysis determines an initial estimate for the boundary layer edge. For each streamwise location along the suction side surface between leading and trailing edges, a series of parameters may be calculated and stored.
- the number of streamwise locations may depend on the resolution of the flowfield. These parameters include the density ⁇ , the velocity U ⁇ and the viscosity ⁇ .
- An integration normal to the surface provides a value of ⁇ and the values of u′, ⁇ X , and Tu may also be calculated and stored.
- the values of Re ⁇ and Re ⁇ onset may then be calculated and stored. The streamwise position where these two values are equal provides the initial estimated transition location.
- a CFD simulation may then be run with the turbulence model shut-off in the flow region upstream of the initial target transition using the boundary determined by the fully turbulent simulation.
- Re ⁇ and Re ⁇ onset are recalculated to determine an updated transition location.
- the boundary layer edge location is updated using the results of the converged solution.
- the CFD simulation is then restarted using the updated target transition location and run to convergence. This process may be repeated with each updated estimate of the transition location until there is convergence of such transition location.
- the pressure distributions and total pressure/temperature changes across the airfoil row may be calculated to determine the performance (e.g., including loss characteristics) of the airfoils of each row and of the multi-row system overall.
- FIG. 2 shows exemplary graphs 400 and 402 of Re ⁇ and Re ⁇ onset , respectively, against the S distance in millimeters for an exemplary airfoil under exemplary conditions. Their intersection 404 determines the streamwise position of transition.
- FIG. 3 shows a graph of experimentally-based values of Re ⁇ onset against Tu ⁇ / ⁇ X , with a curve 406 representing a best fit of the Re ⁇ onset model.
- the experimentally-based values are determined by measuring the streamwise location of onset in cascade tests and then using a laminar model to find the Re ⁇ at such streamwise location.
- FIG. 4 shows the values of Re ⁇ onset against Tu with a Mayle model graph 408 .
- the foregoing attached transition model has its limitations. As airfoil performance is further increased (e.g., enhanced lift of each airfoil permitting reduction in the numbers of airfoils), the airfoils may begin to suffer from laminar flow separations. If the CFD simulations show that the boundary layer separates downstream of the predicted attached-flow transition point, the attached-flow transition point should remain valid. If however the boundary layer separates upstream of the predicted attached-flow transition point, the predicted transition point will likely be invalid. An alternate model is then required to predict the transition location. From a database of experimental cascade and flat plate tests supplemented with CFD-based simulations of the experimental tests, in a range of turbine-specific flow parameters, we have constructed a model to predict the transition location in such a situation. FIG.
- FIG. 5 shows a separation location 50 which may be determined from the CFD simulation described above.
- the transition 32 between laminar and turbulent conditions is shown at a streamwise distance L from the location 50 .
- the streamwise position of location 50 is designated as S sep .
- FIG. 7 shows a plot 410 of the foregoing relationship against experimental data.
- FIG. 8 shows a plot 412 of the Roberts model against such data.
- the Roberts model plots a Reynolds number Re ⁇ against the turbulence intensity multiplied by an exponent (i.e., 0.2) of the quotient of the chord C of the airfoil divided by the turbulence length scale. It can be seen that the Roberts correlation tends to represent a lower limit on the separation size for a given value of Re ⁇ at separation. This means the Roberts model may tend to be biased toward predicting flow reattachment and low loss in cases where stall (and thus high loss) actually occur.
- the present separated boundary layer transition model may be incorporated into the attached flow modeling described above.
- FIG. 9 shows an exemplary flowchart of a process 420 .
- Block 422 identifies a start/resume CFD simulation block. It is followed by a flowfield iteration block 424 which may represent a fixed number of iterations (e.g., 500 iterations) or iterations to a given convergence, or the like. It is followed by block 426 which identifies a pause in the CFD simulation to allow for the processing of the flowfield and the updating of the predicted transition location. This is followed by block 428 which identifies the beginning of a sidewise loop on the suction side of the airfoil to update the transition locations.
- spanwise loop 430 is followed by spanwise loop 430 at discrete locations along the span from the inboard to outboard extremes of the airfoil.
- Subsequent block 432 identifies finding the leading edge flow stagnation location denoting the split between the airfoil pressure and suction sides.
- Subsequent block 434 identifies the calculation of the R ⁇ and R ⁇ onset distributions between the stagnation point and the trailing edge.
- Subsequent block 436 identifies checking for a boundary layer separation and the storing of its location (if any).
- Subsequent decision block 438 identifies the determination of whether a laminar separation exists. If not, a subsequent block 440 identifies the use of prediction from the attached flow model to update the transition location.
- block 442 identifies use of the prediction from the separated flow model to update the transition location. Either block 440 or 442 are followed by a decision block 444 determining whether the spanwise loop is complete. If not, following block 446 identifies incrementing the spanwise location and returning to block 432 for the incremented location. If so, however, decision block 448 determines whether the side-wise loop is complete. If not, the block 450 identifies transition to the other (e.g. pressure) side of the airfoil followed by return to block 430 for such other side. If so, there is returned to block 422 for continued CFD iterations.
- the other e.g. pressure
- FIG. 10 shows a plot 470 for values of the streamwise distance from the stagnation point to transition location (in inches) against the number of CFD iterations. It can be seen that, for this particular case rough stability occurs in the vicinity of 10,000 iterations, with further stability at greater number (e.g. over 15,000) and much less stability at lower numbers (e.g. less than 6,000).
- the foregoing procedure may itself be iterated using manual optimization or optimizer software to reengineer airfoil shape, orientation, and/or number to achieve a desired goal.
- FIG. 11 shows an exemplary plot of loss against Reynolds number for an exemplary airfoil.
- the curve 480 is generally divided into three regions at approximate first and second Reynolds numbers 482 and 484 . In the low Reynolds number region, the losses are high; in the high Reynolds number region the losses are low; and in the mid-level Reynolds number region the loss is transitioning. It is advantageous to optimize the airfoil properties as described above so that the cruise loss level 486 associated with a cruise Reynolds number 488 is as low as possible. This may typically place the cruise Reynolds number near the second Reynolds number 484 , and preferably above it. The optimization may shift the curve 480 locally downward. However, given the high slope in the transition region it may be more useful to shift the intermediate portion toward lower Reynolds numbers notwithstanding that there may be very little (if any) decrease in loss in the high Reynolds number region.
- FIG. 12 shows a baseline airfoil contour with pressure and suction sides/surfaces 200 and 201 and a modified airfoil contour with such sides/surfaces 202 and 203 .
- FIG. 13 shows suction side curvature distributions for the airfoils of FIG. 12 .
- the baseline and modified contours have approximately the same chord and axial length.
- the modified contour is generally thicker, especially the aft 85% or so, with particular thickness increases in the vicinity of 40% axially aft to 70% axially aft.
- the airfoil 202 has fine local surface perturbations which are a result of using ⁇ splines in the optimizer software.
- FIG. 13 shows the modified distribution as having a first trough 220 downstream of an off-scale first (leading edge) peak with a value well under 1.5/inch and more particularly under 1.0/inch. This occurs at a normalized spanwise distance below 0.1 (i.e., the first tenth) and more closely about 0.05.
- a second peak 222 is somewhat over 1.5/inch and occurs at spanwise distance of approximately 0.1.
- a second trough 224 occurs near a spanwise position of 0.2.
- a third peak 226 has a value in excess of 3/inch and well in excess of the downstream peak of the baseline distribution and occurs at a distance of approximately 0.4.
- a penultimate trough 228 occurs with nearly zero curvature at a distance of just over 0.9 and is followed by a sharp ultimate peak 230 of approximately 2.0/inch at a distance of greater than 0.95. Beyond the increased number of peaks and troughs, relative to the baseline distribution the modified distribution has, at a given level of resolution, a greater number of inflection points.
Abstract
Description
where θ is the momentum thickness at such location, ρ is the density at the boundary layer edge at such location, U∞ is the flow velocity at the boundary layer edge at such location, and μ is the viscosity at the boundary layer edge at such location. The turbulence intensity may be identified as:
-
- Tu=100(u′/U∞)
where u′ is the fluctuating component of velocity calculated at the boundary layer edge at such location.
- Tu=100(u′/U∞)
for a variety of turbulence models where A and B are constants that may be associated with a particular model. In one implementation of the k-omega model, A=8.52 and B=−0.956. For any given turbulence model the constants may be determined by substituting in experimental laboratory data from at least two distinct operating conditions.
where C=216 and D=−1.227.
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US20050163621A1 (en) * | 2003-12-20 | 2005-07-28 | Gulfstream Aerospace Corporation | Mitigation of unsteady peak fan blade and disc stresses in turbofan engines through the use of flow control devices to stabilize boundary layer characteristics |
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US20080128561A1 (en) * | 2006-12-01 | 2008-06-05 | Searete Llc, A Limited Liability Corporation Of The State Of Delaware | Active control of a body by altering surface drag |
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